Even More Reasons Why Kites (don't) Fly- Single Line Kite Stability.
There are a large number of effects that influence kite stability (or more usually the lack of). January '09's Newsletter described some fundamental ones. Here are some more:
The approach in "Why kites (don't) Fly- Single Line Kite Stability" was to consider effects from the perspective of how a kite responds when its axis becomes misaligned with the wind direction. Optimally, kites should neither undercorrect (take so long to respond that they get seriously out of position while doing so), nor overcorrect (respond so quickly that dynamic effects can build by positive feedback).
This perspective is not only fundamental to kite stability but usefully leads to explanations as to why particular kites behave (and misbehave) the ways they do. Even more usefully, it leads to predictions as to the effect on stability that possible changes will have. Someday, these may even be quantifiable to some extent.
Line Length: It is the angle of the line relative to wind direction that matters, not line length in the absolute sense- but this angle is a function of the line's length (and the kite's size) so it's usually called the 'line length effect' to avoid using 'line angle', which has multiple association with stability influences.
When a kite is laterally displaced from its proper position directly downwind from the tether point, its line will then have some angle to the wind when viewed from above, and the shorter the line's length, the greater this angle will be. There will then be a component of line tension acting to pull the kite back towards its central position equal to the sine of this angle times the line's projected length. The magnitude of this centralising force is therefore directly proportional to line length for any given lateral displacement of the kite. This will tend to exacerbate any overcorrection tendency and mitigate undercorrection. A more rigorous description requires consideration of the line's angle in the vertical plane also, but the effect is more easily understood in the first instance by considering horizontal angles only. An often experienced practical demonstration of this is when large Cody type box kites (which tend to overcorrect because they have so much lateral area to rearward, though this is masked in normal flying by their high lateral area to lifting area ratio), are being pulled in. By the last few metres of line they are often overcorrecting so violently as to be completely uncontrollable. An opposite example is that kites which are virtually un-flyable because of severe undercorrection can be useable when tethered directly off their bridles- that is, flown on a VERY short line.
Kites don't scale, that is, as they are made bigger, their behaviour changes. Aerodynamic forces increase with the square of the wind speed, but to retain the same margin of strength in proportion to its size as a kite is made bigger, its weight will need to increase with the cube of dimension. So, larger kites will generally be heavier in proportion to their area, and this affects their flying- most obviously in light winds but also in their undercorrection/overcorrection balance. Kites that tend to overcorrect will do this even more so as their weight/area ratio increases. Kites that tend to undercorrect will do this less as their weight/area ratio increases. However, in practise, this can be masked by other effects. A practical demonstration of this is the way that kite behaviour changes in rain- extra weight pushes them toward overcorrection, although this can be masked by fabric stretch effects.
For framed kites, builders very often don't increase the strength and rigidity of the structure proportionally when they make bigger versions. A result of this is that such kites tend to distort more in stronger winds, and the extra drag that this generates may damp out the additional overcorrection that comes from the increasing weight/area ratio. Of course, such kites will also deform so severely as to become un-flyable in wind speeds that their smaller scale version was happy in- or they'll break.
For ram air kites (often called soft kites) up to sizes of even few hundred square metres (that is, VERY large kites by most standards) weight/area doesn't tend to change at all. This is because available fabrics are much stronger than necessary for smaller soft kites. However, the mass of air inside such kites increases with the cube of dimension while their area increases with the square. Mass is not the same as weight in this context. The internal air mass is neutrally buoyant, doesn't make any contribution to the kite's pendulum effect at all, but by Newton's approximation of Einstein's theories, it has inertia, so requires the application of a force to get it to move or to stop moving. For ram air inflated single line kites, the inertia of this air mass proportionally slows the rate of recovery from any misalignment as the kite is scaled up, causing very large ram air inflated kites to tend, often terminally, towards undercorrection. A partial solution to this is to use thru cords rather than ribs by the principle that the internal air mass is then able to rotate (or not rotate) independently to some extent. The kite's weight pendulum when acting to correct a misalignment, isn't then resisted by the inertia of all the internal air mass, but just of those bits trapped in corners. Octopus and Ray kites that were originally rib and skin construction did seem to have less inclination to undercorrection in larger sizes when re-designed using thru cords instead.
Why do stable framed kites seem to be much easier to build than stable soft kites?
Perhaps it's that there are thousands of years of experience behind framed kites and only 50 or so for soft kites, but there are two other reasons (at least):
The first is that closed soft kites tend to have smooth curved upper surfaces in their leading edge areas, which promotes attached flow over the kite's upper surface, significantly increasing the aerodynamic lift that such kites will have. Because the force driving instability for kites is aerodynamic lift, more lift equals less stability (of both the undercorrection and overcorrection type), other things being equal. In contrast, most framed kites have sharp edged leading edges which cause flow to immediately separate and ensures that they will rarely if ever have attached flow over their upper surfaces. This reduces lift and therefore improves stability. By this theory, open leading edge soft kites should tend to be more stable than closed styles (many Parafoils have open leading edges that encourage flow to separate over the top surfaces rather than remain attached ) and they do generally seem to behave better. Why don't we always design soft kites with open leading edges then? There are reasons; like appearance, for more lift (if there's stability to spare), to retain internal inflation in turbulence, and to pressurise against water ingress when flying off boats etc.
The other soft kite effect is that their rigidity keeps pace exactly with aerodynamic forces as wind speed increases- to the limit of fabric impermeability anyway. However, their weight pendulum effect does not increase at all- so will eventually be overwhelmed by these aerodynamic forces. In contrast, framed kite structures deflect progressively more as wind increases, offsetting at least some of the increase in lift forces as the wind speed increases. Framed kites are therefore more likely to remain stable through to higher wind speeds than soft kites. Mike Fardon from Australia, has noticed this effect and reminded me to include it after the January's SLKS. Thankyou Mike.
Von Karman Effects (after the early 20th century German hydrodynamicist). These are airflow driven rhythmic oscillation that, in our case, causes cylindrical form kites to oscillate in some wind speeds. The most easily recognisable every day von Karman effect is the "vortex street" visible downstream of a post sticking out of a stream. When encountering the post, flow splits evenly, half going around each side. However, because of inevitable asymmetries in the post, the flow, and the universe, the split streams don't arrive back at the downstream side at quite the same moment. The flow stream that arrives first then continues to be sucked around the post until it is, from an above observer's perspective, moving upstream against the main current. At some point it then finds this situation unsustainable, separates from the pole surface and is carried off downstream, turbulently. The opposite side stream then has its turn and repeats the process. The above observer will see this as a succession of alternating turbulent eddies drifting off downstream and gradually re-merging with the stream's flow. An effect of this is that the pole (in this case) will be subject to oscillating sideways forces as each vortex separates. Industrial chimneys have spiral flow interrupters on their upper reaches to prevent this rhythmic effect becoming destructive. I think that many large ram air inflated kites are subject to von Karman effects- Dolphin and Gecko styles in particular. Any kite for which airflow passes around some even approximately cylindrical form is likely to be. I should test this by using smoke trails, but haven't as yet. I expect it is right though, because another characteristic of von Karman oscillations is clearly observable on these kites. This is that as wind speed increases, the lateral oscillations decrease and eventually cease completely, probably because at higher wind speeds, flow separates chaotically rather than periodically and also because the flow period gets out of synch with the kite's mass. When oscillations are being caused by some dynamic effect of overcorrection, they tend to continue to increase with wind speed until the kite loops out. A way to eliminate von Karman effects is to have some feature that causes separation, like long fins for a fish kite. For themed kites, unfortunately, anatomical requirements often make such features unacceptable.
Speed Sensitive Aerodynamic Damping. There is a diverse group of aerodynamic features that can act to damp out dynamic effects. Because they don't kick in until one of the kite's wings is travelling significantly faster than the other, they don't change the kite's fundamental overcorrection/undercorrection balance. Rather, they do allow kites with significant overcorrection responses to resist the build up of destructive dynamic figure-eighting that would otherwise occur. Because having a fast response to misalignment is desirable in a kite providing that dynamic effects don't then get away, these are very useful tools for kite designers to have available.
Delta kites have a version. When a Delta style kite starts to figure eight with increasing amplitude, the faster moving wing tip will have more load on it than the opposite slower one. This asymmetry of load distorts the kite's form, causing the faster wing tip to twist off more, generate less lift and proportionally more drag. The slower wing tip will respond oppositely- generate more lift and less drag. This reduces the speed difference between the tips, damping out a dynamic build up that could otherwise become destructive.
Rokaku kites have a similar mechanism. When one side of a Rokaku experiences higher apparent wind speed than the other side, asymmetry of aerodynamic forces causes the faster side to increase its camber and the slower side to flatten off. This increases the drag and decreases the lift on the faster side and decreases the drag and increases the lift on the slower side, which, as for the Delta mechanism, acts to prevent destructive dynamic effect building up.
Many framed kite styles have this type of automatic built in dynamic damping, but soft kites don't, except that most closed soft kites get some dynamic damping from internal pressure not holding inflation as well against external pressure on their faster wing's leading edge as on the slower side. Differential speed sensitive air brakes could be fitted to the wings of soft kites to damp dynamic effects in the same way that the relationship between structures and skin do for Deltas and Rokakus. I've tried a few ideas for these and will do more work in this area when I get time (like by not going to so many kite festivals, yeah right!). Potentially differential air brakes should be able to offset a lot of the stability deficit that closed soft kites often seem to exhibit by comparison to open leading edge soft kites, and even to framed kites.
More Commentaries later, and yes, Reynolds number effects are on the list.
Peter Lynn, Ashburton, 2 March '09
PS I have a new kite design; It's a Ray for UKS (Ultimate Kite Show) designed to be more recognisable, by appearance and movement and built without any trailing drag devices to catch water while launching and retrieving from boats. It is the first kite I've designed using the stability theories from January and above as the starting point. In the past I've generally just built each new design then tried to cure misbehaviour afterwards, while staying within graphic constraints. I'm not yet sure that the new ray will be successful. It flies in light wind and in strong, looks great, and moves realistically. But it has a tendency to hang to one edge, then recover and fly to the opposite edge and so on, repeating, rather than to fly centrally while swimming a little. I don't think this is classic undercorrection- because it's accompanied by complete folding over of one or the other wing tip, either inwards or outwards, depending on the lengths of the tip bridles. I can't add any trailing drag elements though, and want to retain the wing flapping motion, so options are rather limited- a challenge!